A Study of Trastuzumab Emtansine Versus Taxane in Participants With Human Epidermal Growth Factor Receptor 2 (HER2)-Positive Advanced Gastric Cancer

Inclusion Criteria:

* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Life expectancy of at least 12 weeks from the first dose of study treatment
* Measurable and/or evaluable disease based on Response Evaluation Criteria in Solid Tumors (RECIST version 1.1)
* Adequate organ function as determined by the following laboratory results, within 28 days prior to randomization
* Participants must have a history of advanced gastric cancer (AGC), defined as unresectable and locally advanced or metastatic gastric cancer, including adenocarcinoma of the gastroesophageal junction (GEJ), and must have experienced disease progression during or after first-line therapy for their disease
* HER2-positive tumor (primary tumor or metastatic lesion) as confirmed by central laboratory HER2 testing (immunohistochemistry and/or in-situ hybridization)
* Participants must have received at least one prior chemotherapy regimen for AGC; prior therapy does not need to have included HER2-directed therapy.
* First-line therapy for AGC, including adenocarcinoma of the GEJ, must have included a combination of at least a platinum- and a fluoropyrimidine-based treatment given concurrently; prior therapy does not need to have included a HER2-directed therapy.
* Adjuvant or neoadjuvant therapy for AGC is allowed.

Exclusion Criteria:

* An interval shorter than 21 days from the last dose of chemotherapy or HER2-directed therapy until the time of randomization
* Prior treatment with trastuzumab emtansine, docetaxel, or paclitaxel either as single agents or as part of a treatment regimen.
* Treatment with any investigational anticancer drug within 21 days of the first study treatment administration
* More than one prior line of therapy for advanced gastric cancer
* History of other malignancy within the previous 5 years except for appropriately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, Stage I uterine cancer, or other malignancies with an expected curative outcome
* Brain metastases that are untreated or symptomatic or require any radiation, surgery, or steroid therapy to control symptoms from brain metastases within 1 month of randomization
* Peripheral neuropathy Grade \>/=2
* Uncontrolled cardiopulmonary dysfunction (e.g., high blood pressure, serious cardiac arrhythmia)
* Other current, severe, uncontrolled systemic disease (e.g., clinically significant metabolic disease, wound healing disorders, ulcers)
* Clinically significant bleeding within 30 days before enrollment
* For female participants, current pregnancy or lactation
* Major surgical procedure or significant traumatic injury within 28 days prior to randomization or anticipation of the need for major surgery during the course of study treatment
* Infection with Human immunodeficiency virus (HIV) or hepatitis B virus, hepatitis C virus